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Rutherford’s model of the atom
Rutherford published his model of the atom [1] in
1911 as an interpretation of the α-scattering work carried
out by Geiger and Marsden [3] two years earlier.
�e puzzle centred on finding a convincing explanation
for the small fraction of α particles (around 1 in
20,000) which were deflected through large angles,
a�er passing through gold foil only 0.00004 cm thick.
He argued that the probability of occasional largeangle
scatters was inconsistent with multiple small angle
scattering, and could only be explained by a single scattering
event. �is required an“intense electric field”and
led him to propose his model of an atom with a charge
of ±Ne at its centre surrounded by a uniformly distributed
sphere of the opposite charge.
His arguments did not depend on the charge at the centre,
but he chose the correct sign: “...the main deductions of
the theory are independent of whether the central charge
is supposed to be positive or negative. For convenience,
the sign will be assumed to be positive.” He was aware that
there were unanswered questions about how such a structure
could exist: “�e question of the stability of the
atom proposed need not be considered at this stage…”
�ese questions were only fully answered much later.
Using a reasonable estimate for the nuclear charge he
calculated the distance of closest approach (~34 fm) for
a typical head-on α particle to be completely stopped
and provided the first ever order-of-magnitude estimate
of the size of the nucleus. He showed that the trajectory
taken by an α particle was hyperbolic and related the
angle of deviation δ to the perpendicular distance b between
the line of approach and the centre of the nucleus.
He showed the scattering probability was proportional
to cosec 4 (δ/2) and inversely proportional to the 4 th
power of velocity. An important test of his model was
to calculate the dependence of the relative number of
scattered particles n on the atomic weight A. �e ratio
n/A 2/3 should be constant. �e measured values for eight
elements between Al and Pb ranged from 208 to 250
with an average of 233. He concluded: “Considering the
difficulty of the experiments, the agreement between
theory and experiment is reasonably good.”
Following the publication of his ground-breaking paper
[1], Rutherford worked closely with other leading physicists
of the day.Niels Bohr visited Manchester in 1912 and
again 1914-16. Bohr’s model of stationary non-radiating
electron orbits [4] added credence to Rutherford’s atom
and answered the question of why the electrons do not
fall into the nuclear core. Subsequent developments in the
theory of quantum mechanics gave this an even sounder
footing.However,understanding the small size and strong
binding of the nucleus would have to wait till the 1930s,
when the neutron was discovered and Yukawa first described
the strong attractive force binding neutrons and
protons together in terms of meson exchange.
� fig. 1:
Photograph of
Hans geiger (left)
&ernestrutherford
(right) in their
laboratory at
manchester university
circa 1908.
� fig. 2: The α
particle, experiencing
an inverse
square repulsive
force, follows a
hyperbolic trajectory
(green) as it
approaches the
nucleus located
at S, the external
focus of the
hyperbola. it
enters along the
asymptotic direction
Po (red)
reaching its closest
approach
d=Sa at the apse
of the hyperbola
before exiting
along the second
asymptote oP’.
The angle of deviation
δ=π-2θ
depends on the
energy of the
alpha particle
and its impact
parameter b=Sn.
EPN 42/5 19